让贝叶斯优化聚焦可搜索路径，提升局部优化效率。
Local Entropy Search over Descent Sequences for Bayesian Optimization
- 基于下降序列的后验传播，建模可到达解的分布
- 在高复杂度任务中样本效率优于主流方法
- 适合需高效探索局部最优的设计空间
在大规模复杂设计空间中寻找全局最优可能不可行且不必要。一种实用替代方案是使用梯度下降等局部优化方法，逐步细化初始设计的邻域。本文提出局部熵搜索（LES），一种贝叶斯优化范式，明确针对迭代优化器可生成的下降序列进行搜索。算法通过优化器传播目标函数的后验信念，得到下降序列的概率分布，并通过最大化与该分布的互信息选择下一个评估点，结合解析熵计算与蒙特卡洛采样下降序列。在高复杂度合成目标和基准问题上的实验表明，相比现有局部与全局贝叶斯优化方法，LES展现出优异的样本效率。
原文摘要 · Abstract (English)
Searching large and complex design spaces for a global optimum can be infeasible and unnecessary. A practical alternative is to iteratively refine the neighborhood of an initial design using local optimization methods such as gradient descent. We propose local entropy search (LES), a Bayesian optimization paradigm that explicitly targets the solutions reachable by the descent sequences of iterative optimizers. The algorithm propagates the posterior belief over the objective through the optimizer, resulting in a probability distribution over descent sequences. It then selects the next evaluation by maximizing mutual information with that distribution, using a combination of analytic entropy calculations and Monte-Carlo sampling of descent sequences. Empirical results on high-complexity synthetic objectives and benchmark problems show that LES achieves strong sample efficiency compared to existing local and global Bayesian optimization methods.
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